chore: update tryUnlockMetamask action to use async background calls

[davidmurdoch]

Description

Related issues

Fixes:

Manual testing steps

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Screenshots/Recordings

Before

After

Pre-merge author checklist

• I've followed MetaMask Contributor Docs and MetaMask Extension Coding Standards.
• I've completed the PR template to the best of my ability
• I’ve included tests if applicable
• I’ve documented my code using JSDoc format if applicable
• I’ve applied the right labels on the PR (see labeling guidelines). Not required for external contributors.

Pre-merge reviewer checklist

• I've manually tested the PR (e.g. pull and build branch, run the app, test code being changed).
• I confirm that this PR addresses all acceptance criteria described in the ticket it closes and includes the necessary testing evidence such as recordings and or screenshots.

[github-actions]

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